The scalar product and the vector product
The scalar (dot) product of two vectors is a number that tells us the angle between them; the vector (cross) product is a vector perpendicular to both. Work out both and use them.
- سوريا: الصف ١١
- فلسطين: الصف ١١
- إيران: الصف ١٢
- أفغانستان: الصف ١١
- أوكرانيا: الصف ١٠
- روسيا: الصف ٩
- ألمانيا: الصف ١٢
- فرنسا: الصف ١١
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
This studio follows the last two lessons of Afghan Year 11 chapter 7, Iran's Year 12 geometry chapter 3 and Further Maths. The الجداء السلمي of two vectors is a number: multiply matching components and add them with their signs. It equals |a||b|cosθ, where θ is the angle between the vectors. If the product is zero the vectors are perpendicular.
The الجداء الشعاعي of two vectors is a vector perpendicular to both. We write it as a 3 × 3 determinant whose first row is i, j and k; the j component takes a minus sign. Its length is the area of the parallelogram the two vectors make.
Common mistakes: losing the signs of negative components, and forgetting the minus sign on the j component of a cross product.